How did paine and jefferson use the concepts of equality, reason and nature to criticize the legitimacy of monarchical government and british control of the colonies?

They both controlled the British colonies and they have the power over the patriots.

They both believed the selection of kings to be unnatural because people are born as kings and nothing assures that they'll be good leaders. They argued  that nature disapproves otherwise there wouldn't be "an as for a lion".

Hope this helps!